What
is the Tangram
The Tangram is nowadays the most popular dissection puzzle formed
from 7 polygons. The aim of the puzzle is to seamlessly arrange all the geometric
pieces to form problem figures (rules
of the game). More than 100 years ago, this game was as famous as
the Rubik
cube and has been played passionately by many as entertainment, educational
or mathematical tool, because it boosts shape recognition, problem solving, and
pattern design skills. It is said that the Pythagorean theorem was discovered
in the Orient with help of Tangram pieces...
The 7 polygons or 'tans' (see image further below)
that form the Tangram are:
• 5 right triangles:
2 small (hypotenuse of n/2 and sides of n/2√2); 1 medium
(hypotenuse of n/√2 and sides of n/2); 2 large (hypotenuse
of n and sides of n/√2). The large triangle is 4 times
the size of the small triangle, but curiously its perimeter is only 2 times as
big!
• 1 square (side of n/2√2).
• 1 parallelogram/rhomboid (sides
of n/2 and n/2√2).
Of these 7 pieces, the parallelogram (or rhomboid) is the only piece
that may need to be flipped when forming certain shapes; in fact, it has no reflection
symmetry but only rotational symmetry, and so its mirror image
can only be obtained by flipping it over.

Aim
of the puzzle The
object of the Tangram game is to put the seven geometric shapes
together so as to form a given outline/silhouette (rules
of the game). Sometimes there is more than one solution.
Alternative solutions are accepted as long as they have EXACTLY
the same outline of the matching figure. For instance, the two
pink figures opposite seem identical but are in fact NOT the
same.

First
challenge
Print this page and cut out the 7 shapes below. Then, try with all
7 pieces to compose a perfect square (there are several solutions, this one is
a classic).

Once
you have tried that, see if you can form a larger square using
the above 'tans' and adding the extra shape 1)
below... Can you do the same using shape 2)?
or shape 3)?

3
additional pieces

(Click
on the shapes above to see solutions)

Short
history of the Tangram

Little
is known for certain about the origin of the Tangram. Even
the origin of the name is obscure! The earliest known book
was published in 1813 in China, but the publication date
is not reliable. Nevertheless, one Tangram-like puzzle first
appeared in a book published in Japan in 1742.
Scholars assume that Tangram began in the Orient before the 18th
century and then spread westward. Frankly, in my humble opinion, a lot of 'oriental'
games were first created in Europe and then readapted in Asia, like the "Chinese
checker", called tiao-qi in China (the "Chinese checker" was
actually invented in Germany in 1892 and is a descendant from the game Halma)...
In the past, the adjective 'Chinese' was commonly used to denote any odd, complicate
or contrived thing and not the origin! However, by 1817, Tangram publications
had appeared in the United States and in Europe. Whatever date the Tangram was
invented, you have to know that rearrangement puzzle roots can be traced back
to the 3rd century BC! Back in those days, Archimedes, a Greek mathematican,
designed a Tangram-like puzzle called Loculus
Archimedis or Ostomachion.
Toward the end of 19th century, Friedrich Ad. Richter, a German industrialist,
began to manufacture stone versions of Tangram along with other dissection puzzles
under the name of 'The
Anchor Puzzle' (Anker). The Anchor puzzles were so successful that
over 30 new designs of puzzle sets followed.

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are welcome to use whatever you want from this page, but
please CREDIT us! Please note that you can print and reproduce
the content of this page in unaltered form only for your
personal, non-commercial use. We would appreciate receiving
any comment,
suggestions or corrections concerning our Tangram pages.
Thanks!